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Fermion Masses and Unification

Fermion Masses and Unification. Steve King University of Southampton. Lecture 2. Unification. Most popular Groups are:. Quarks, Leptons. Quarks, Leptons, right-handed neutrino. Quarks, Leptons, exotics, SM singlet,. GUTs. Simple Group.

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Fermion Masses and Unification

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  1. Fermion Masses and Unification Steve King University of Southampton

  2. Lecture 2 Unification

  3. Most popular Groups are: Quarks, Leptons Quarks, Leptons, right-handed neutrino Quarks, Leptons, exotics, SM singlet, GUTs Simple Group Quarks and Leptons unified into representations of

  4. Simple Group GUTs Single coupling constant spontaneously broken: Couplings assumed to ‘run’ to measured SM couplings If no additional (non-SM singlet) fermions are added: At GUT energy. Applies to all three examples

  5. GUTs

  6. Georgi and Glashow SU(5) GUT With the hypercharge embedding Each family fits nicely into the SU(5) multiplets N.B in minimal SU(5) neutrino masses are zero. Right-handed neutrinos may be added to give neutrino masses but they are not predicted.

  7. Gauge Sector of SU(5)

  8. Summary of Matter and Gauge Sector of SU(5)

  9. Higgs Sector of SU(5) Candidate Higgs reps of SU(5) are contained in matter bilinears constructed from 5* and 10 Minimal suitable Higgs reps for fermion masses consist of 5H + 5*H

  10. The smallest Higgs rep which contains a singlet under the SM subgroup is the 24 Higgs rep and is a candidate to break SU(5) The Higgs superpotential involving the minimal Higgs sector of SU(5) consisting of the 24H plus 5H plus 5H* With some tuning (see later) one can achieve light Higgs doublets which can develop weak scale vevs

  11. The Yukawa superpotential for one family with Higgs H=5, H*=5* good bad c.f. good SUSY relations at MGUT: mb¼ m , ms¼ m/3 , md¼ 3me

  12. Pati-Salam Partial Unification

  13. The Yukawa superpotential for one family at the GUT scale Could work for the third family, but certainly not for all three families at the GUT scale is bad at the GUT scale is almost good

  14. Georgi-Jarlskog Textures Gives good SUSY relations at MGUT: mb¼ m , ms¼ m/3 , md¼ 3me Gives GJ factor of -3 for the lepton

  15. Summary of Pati-Salam -- Predicts RH neutrinos with lepton number as the “fourth colour” -- Allows the possibility of restoring parity if LR symmetry is imposed -- (Quark-lepton) unification of 16 family into two LR symmetric reps -- B-L as a gauge symmetry -- Quantization of electric charge  Qe= -Qp -- Pati-Salam can be unified into SO(10)

  16. SO(10) GUT Georgi; Fritzsch and Minkowski The 16 of SO(10) contains a single quark and lepton family and also predicts a single right-handed neutrino per family. The SU(5) reps are unified into SO(10): The two Higgs doublets are contained in a 10 of SO(10)

  17. Neutrino masses in SO(10) Dirac mass Heavy Majorana mass SO(10) contains all the ingredients for the see-saw mechanism and tends to predict a hierarchical pattern of neutrino masses

  18. Triplet Higgs Like ‘matter’ particles, Higgs must be embedded into representations of e.g. Leads to new (triplet) particles D. All give new particles: , Spoil Unification of MSSM gauge couplings 1 Problems: 2 Cause rapid proton decay

  19. Proton Decay with triplets Say representation of And quarks and leptons representation of To produce SM Yukawa terms one generally uses terms Gives following SM interactions: But also gives ‘dangerous’ terms involving with SM particles: Proton decay

  20. D-exchange generates superfield operators In terms of scalar and fermion components some examples of dangerous operators are shown below

  21. Minimal SU(5) is ruled out by proton decay -- but it gives unacceptable fermion masses anyway

  22. a a b Doublet triplet splitting? Two possible types of solutions: Give large GUT scale masses to Doublet-Triplet splitting Allow TeV scale masses to but suppress interactions b Yukawa suppression is required ‘Solves’ Proton Decay and Unification problems ‘Solves’ Proton Decay problem but leaves Unification problem

  23. DT Splitting problem Nontrivial to give huge masses to but not e.g. most simple mass term would be in Minimal superpotential contains: Superpotential: GUT EW scale Fine tuning to within 1 part in 1014

  24. And in direction gives mass couplings to DT Splitting solution ‘Missing – partner’ mechanism’ Pair up H with a G representation that contains (colour) triplets but not (weak) doublets (at least after G is broken). Take superpotential to contain: Under : 50 contains (3,1) but not (1,2) Nothing for Higgs hu , hd to couple to Problems: Large rank representations problem for Higgs mass Proton decay via triplet Higgsino from effective term.

  25. GUTs with light triplets • The  problem (light Higgs mass) is intimately related to the doublet-triplet splitting problem (heavy triplet mass) • One approach is to allow both light Higgs doublets and triplets • Requirements: generate TeV scale mass terms for the light Higgs doublets and triplets, suppress proton decay due to triplet exchange while allowing triplets to decay in less that 0.1 s to avoid problems with nucleosynthesis • The Exceptional Supersymmetric Standard Model (ESSM) is an example of a model with extra low energy exotic matter forming complete 27’s of E6 plus the two Higgs doublets of the MSSM: • [5*+10+ (5+5*)+1+1]xthree families +(H,H’) Quarks, leptons Triplets,Higgs, singlets Non-Higgs 27

  26. MString E8£ E8! E6 MGUT E6! SU(5)£U(1)N Right handed neutrino masses Quarks, leptons Triplets and Higgs Singlets and RH s H’,H’-bar Incomplete multiplets (required for unification) TeV U(1)N broken, Z’ and triplets get mass,  term generated MW SU(2)L£ U(1)Y broken ESSM= MSSM+3(5+5*)+Singlets Right handed neutrinos are neutral under: ! SM £ U(1)N

  27. Most general E6 allowed couplings from 273: FCNC’s due to extra Higgs Allows p and D,D* decay Family Universal Anomaly Free Charges:

  28. Rapid proton decay + FCNCs extra symmetry required: • Introduce a Z2under which third family Higgs and singlet are even all else odd  forbids W1 and W2 and only allows Yukawa couplings involving third family Higgs and singlet • Forbids proton decay and FCNCs, but also forbids D,D* decay so Z2must be broken! • Yukawa couplings g<10-8 will suppress p decay sufficiently • Yukawa couplings g>10-12 will allow D,D* decay with lifetime <0.1 s (nucleosynthesis) • This works because D decay amplitude involves single g while p decay involves two g’s

  29. Blow-up of GUT region Unification in the MSSM 2 loop, 3(MZ)=0.118 MSUSY=250 GeV

  30. Blow-up of GUT region Unification with MSSM+3(5+5*) 2 loop, 3(MZ)=0.118 1.5 TeV 250 GeV

  31. MESSM= 3x27’s (no H,H’) MPlanck E6! SU(4)PS£ SU(2)L£ SU(2)R £ U(1) MGUT SU(4)PS£ SU(2)L£ SU(2)R£ U(1)! SM £ U(1)X x three families Right handed neutrino masses Quarks, leptons Triplets and Higgs Singlet TeV U(1)X broken, Z’ and triplets get mass,  term generated MW SU(2)L£ U(1)Y broken

  32. Planck Scale Unification with 3x27’s MPlanck MPlanck Low energy (below MGUT) three complete families of 27’s of E6 High energy (above MGUT»1016 GeV) this is embedded into a left-right symmetric Pati-Salam model and additional heavy Higgs are added.

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